Exam 10: Simulation Modeling

Use this information to answer the following questions. The Gambler Hotel in Las Vegas has 300 rooms that each rent for $175 per night.For each reservation accepted,there is a 7% chance that the guest will not arrive.If the hotel overbooks,it incurs $220 for each reservation that is not honored. -Refer to the information above.Suppose that the hotel's manager believes that accepting 320 nightly reservations is a policy that the hotel should implement.Use Crystal Ball to estimate the average daily profit using the manager's policy.Use 1000 replications.

A handyman specializes in fixing plumbing and electrical problems.Assume that 40% of the service calls that he gets relate to electrical problems,while 60% of the service calls relate to plumbing problems.On average,the time it takes to fix an electrical problem can range between 15 and 45 minutes,where all values between the minimum and maximum occur with equal likelihood.Moreover,the time it takes to fix a plumbing related problem can take a minimum of 15 minutes and a maximum of 60 minutes,where 30 minutes is the most probable time. a.Use Crystal Ball to find the average time it takes the handyman to fix a given service call.Use 1000 replications. b.What is the probability that it will take the handyman more than 45 minutes to complete a given service call?

What are output measures called in Crystal Ball?

An insurance company derives its revenues from its three primary business units: home insurance,auto insurance,and life insurance.The revenues for the year ending 2005,along with the potential growth rates per business unit for 2006 are illustrated below. Business Unit $\quad \underline { 2005 \text { Revenues } } \quad \underline { 2006 \text { Growth Rates } }$ Home Insurance $\quad \$ 500,000 \quad$ Normal; $\mu = 7 \% , \sigma = 2 \%$ Auto Insurance $\quad \$ 450,000 \quad$ Triangular, $\min = 2 \% , \max = 6 \%$ , $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ most probable $= 4 \%$ Life Insurance $\quad \$ 550,000 \quad$ Uniform, min $= 4 \% , \max = 10 \%$ a.Use Crystal Ball to simulate total revenues for 2006.Run 1000 replications of the model to find the average revenues. b.What is the probability that 2006 revenues will exceed $1.6 million?

Use this information and output to answer the following questions. Rentals-R-Us specializes in 4WD car rentals.The number of rentals per month typically ranges between 10 and 50.You may assume equal probability for the number of rentals to assume any value in that range.The monthly operating costs for Rentals-R-Us can range anywhere from $2,000 to $4,000,with $3,000 being the most probable cost.Each rented vehicle generates $55 in revenues.You decide to build a simulation model in Crystal Ball to simulate monthly profits. A B 1 Rentals-R-Us 2 Number of car rentals 50 3 Rental per car \ 55 4 Monthly operating costs \ 2,000 5 Profit or loss \ 750 -Refer to the table.Which cell(s)would be designated as the "Forecast cell"?

The probability that a sniper hits his target is 80%.If three snipers aim at the same target,use Crystal Ball to compute the odds that all three snipers will hit their target.Use 1000 replications.

Replicating a model about 20 times is adequate for the simulation results to be valid and useful.

In a game of backgammon,your movement is based on the outcome that you get from rolling a pair of dice.Tossing a pair of sixes on the very first roll will give you a significant initial advantage over your opponent.Use Crystal Ball to determine the odds of rolling a pair of sixes in 1000 simulation runs.

Use this information to answer the following questions. A call center receives an average of 20 calls per minute.You may assume that the numbers of calls are independent of each other,and that the average number of calls remains the same for each minute interval. -Refer to the information above. a.What type of distribution describes the number of calls received? b.Use Crystal Ball to simulate the number of calls received per minute.Use 1000 replications. c.What is the probability that the call center will receive more than 30 calls per minute? d.What is the probability that the call center will receive less than 25 calls per minute?

In Excel,the function =NORMINV(RAND(),100,5)will return a normally distributed random number with a standard deviation of 100 and mean of 5.

Crystal Ball's CB.Custom function can be used to simulate discrete uniform random values.

An assembly plant has experienced the following daily absenteeism over the past 30 days. Nurmber of Employees Absent 0 1 2 3 4 Nurmber of Days 4 6 10 4 6 a.Use the historical data to estimate the probability distribution of absenteeism. b.What is the theoretical expected absenteeism? c.Use Crystal Ball to simulate 1000 sample absenteeism values. d.Compare the mean of the 1000 sample values with the theoretical expected mean.

Cheap Rentals has collected the following information on the demand for compact cars over the last 30 days. Daily Demand 10 11 12 13 14 Number of Days 5 7 8 5 5 a.Use the historical data to estimate the probability distribution of demand for compact cars. b.What is the theoretical expected demand? c.Use Crystal Ball to simulate 1000 sample demand values. d.Compare the mean of the 1000 sample values with the theoretical expected mean.

Suppose that the time needed to complete a final examination in a particular course is normally distributed with a mean of 60 minutes and a standard deviation of 10 minutes. a.Use Crystal Ball to simulate 1000 test scores. b.What is the probability of completing a test in less than 60 minutes? c.What is the probability of completing a test between 50 minutes and 70 minutes?

A binomial distribution can yield only two outcomes.

When rolling a die once,what is the probability that the face of the die is odd? Use Crystal Ball to simulate the event of rolling a single die 1000 times in order to compute the requested probability.

Simulation results can produce different solutions in repeated runs.

Use this information to answer the following questions. A supermarket stocks 150 apple pies each week.Weekly demand for apple pies ranges between 90 and 160 pies,all occurring with equal probability.Each unsold pie incurs an inventory carrying cost of $2.00.Unmet demand costs the supermarket $4.00 per pie. -Refer to the information above.Use Crystal Ball to find the average weekly costs (i.e. ,shortage and carrying costs)if the supermarket stocks 150 pies weekly.

Use this information and output to answer the following questions. Rentals-R-Us specializes in 4WD car rentals.The number of rentals per month typically ranges between 10 and 50.You may assume equal probability for the number of rentals to assume any value in that range.The monthly operating costs for Rentals-R-Us can range anywhere from $2,000 to $4,000,with $3,000 being the most probable cost.Each rented vehicle generates $55 in revenues.You decide to build a simulation model in Crystal Ball to simulate monthly profits. A B 1 Rentals-R-Us 2 Number of car rentals 50 3 Rental per car \ 55 4 Monthly operating costs \ 2,000 5 Profit or loss \ 750 -Refer to the table.What is the appropriate distribution for the variable "Number of car rentals"?

Monte Carlo simulation and operational gaming are the only two categories of simulation.